The plans, called Medicare Advantage, are offered by health insurance companies as an alternative to traditional, government fee-for-service Medicare. Nearly 12 million seniors are in private Medicare health plans, about 25 percent of all Medicare beneficiaries.

Enrollment in the plans is expected to grow by 10 percent in 2012, said Jonathan Blum, deputy administrator for the Centers for Medicare and Medicaid Services.

Open enrollment in the Medicare health plans starts Oct. 15, a month earlier than in past years. It will run though Dec. 7.

Lower premiums and enrollment growth in the plans is the exact opposite of what health insurers predicted would happen after the federal health law was enacted. It reduces payments to the plans by $145 billion over a decade.

Many critics had raised fears that Medicare benefits would shrink and premiums would rise. Instead we are seeing just the opposite," said Health and Human Services Secretary Kathleen Sebelius. "Medicare plans are stronger than ever and beneficiaries continue to have access to affordable options."

Last month, the administration said premiums for private Medicare prescription drug plans would fall slightly, too.